Problem 13: An agent for a residential real estate company in a large city would
ID: 3149786 • Letter: P
Question
Problem 13:
An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost for apartments, based on the size of an apartment, as defined by square footage. The agent selects a sample of 25 apartments in a particular residential neighborhood and gathers the data below (stored in Rent).
i) Calculate and interpret the meaning of b0 and b1 in this problem.
ii) Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet?
APARTMENT
MONTHLY RENT ($)
SIZE (SQUARE FEET)
APARTMENT
MONTHLY RENT ($)
SIZE (SQUARE FEET)
1
950
850
14
1,800
1,369
2
1,600
1,450
15
1,400
1,175
3
1,200
1,085
16
1,450
1,225
4
1,500
1,232
17
1,100
1,245
5
950
718
18
1,700
1,259
6
1,700
1,485
19
1,200
1,150
7
1,650
1,136
20
1,150
896
8
935
726
21
1,600
1,361
9
875
700
22
1,650
1,040
10
1,150
956
23
1,200
755
11
1,400
1,100
24
800
1,000
12
1,650
1,285
25
1,750
1,200
13
2,300
1,985
APARTMENT
MONTHLY RENT ($)
SIZE (SQUARE FEET)
APARTMENT
MONTHLY RENT ($)
SIZE (SQUARE FEET)
1
950
850
14
1,800
1,369
2
1,600
1,450
15
1,400
1,175
3
1,200
1,085
16
1,450
1,225
4
1,500
1,232
17
1,100
1,245
5
950
718
18
1,700
1,259
6
1,700
1,485
19
1,200
1,150
7
1,650
1,136
20
1,150
896
8
935
726
21
1,600
1,361
9
875
700
22
1,650
1,040
10
1,150
956
23
1,200
755
11
1,400
1,100
24
800
1,000
12
1,650
1,285
25
1,750
1,200
13
2,300
1,985
Explanation / Answer
i) I have used excel for the analysis.
Beta0=177.1208, this means that when size is 0, even then rent is 177.1208
Beta 1=1.0651, this means that when size chnages by 1 unit, the rent changes by 1.0651 units.
The model is rent=177.1208+1.0651*size
2) there is no data point that is 500. Hence this model may not produce reliable results for those apartments.
Regression Analysis r² 0.723 n 25 r 0.850 k 1 Std. Error 194.595 Dep. Var. MONTHLY RENT ($) ANOVA table Source SS df MS F p-value Regression 2,268,776.5453 1 2,268,776.5453 59.91 7.52E-08 Residual 870,949.4547 23 37,867.3676 Total 3,139,726.0000 24 Regression output confidence interval variables coefficients std. error t (df=23) p-value 95% lower 95% upper Intercept 177.1208 161.0043 1.100 .2827 -155.9419 510.1835 SIZE (SQUARE FEET) 1.0651 0.1376 7.740 7.52E-08 0.7805 1.3498